When a plant has a strong nonlinear property, a high precision control cannot readily be realized because of tracking and/or stability problems when a general linear feedback controller such as PD, PID or the like is used. For example, as for a variable lift mechanism of an engine, a high precision feedback control cannot readily be realized because the variable lift mechanism has a large friction and a nonlinear property such as a hysteresis characteristic against an increase/decrease of the lift amount. Similarly, a variable phase mechanism and/or an air/fuel ratio control mechanism for an engine and an actuator control mechanism of an automatic transmission have strong nonlinearity.
Because the engine control depends on realization of high precision operations of each of multiple components of the engine, a high precision in stability of behavior and tracking capability is required for the components having a strong nonlinearity such as described above. Thus, there is a need for a control technique for a plant having a strong nonlinear property.
For example, the Japanese Patent Application Publication No. 2001-152885 discloses a control technique using a sliding mode controller in which a dither input is added. This control technique uses the dither input to correct a controlled variable that is calculated from the sliding mode controller to perform a feedback control of the plant toward a desired value. Through this process, a decrease in the controllability, which may be caused by the nonlinear property of the plant such as the friction property or the like, can be compensated.
According to the above technique, however, only a dither input having predetermined amplitude is added to the controlled variable when a switching function of the sliding mode controller exceeds a threshold value. In other words, when the plant approaches to the desired value (when the switching function is below the threshold value), the addition of the dither input is suspended, so the control becomes equivalent to the usual feedback control. For this reason, tracking delay and occurrence of a steady-state deviation are not prevented although behaviors during the feedback control are smoothed out. Besides, if the dither is added and the amplitude of the dither signal is set to be larger even when the switching function is below the threshold value in order to resolve the above-described problem, vibration may occur around the desired value.
A similar control technique, a ΔΣ modulation algorithm is commonly known (for example, refer to the Japanese Patent Application Publication No. 2003-195908). This technique uses, as a control input, a modulation signal that is a binary signal converted from a reference input signal from a controller. According to this technique, as long as a plant is capable of reproducing on/off inputs, a nonlinear property can be compensated to make a precise control of the output of the plant regardless of the degree of its responsiveness.
However, in order to realize high controllability over the whole range of the reference input signal generated by the controller, the modulation signal is required to have a larger variation range than the reference input. As a result, in case of a plant such as a variable lift mechanism in which the variation range of the reference input is larger and the speed of the variation is faster, the absolute value of the generated modulation signal may become larger. In such case, even for the stable desired value, the control input may vibrate and accordingly the output of the plant may vibrate.